DISTILLATION COLUMN DESIGN
As mentioned, distillation columns are designed using
VLE data for the
mixtures to be separated. The vapour-liquid equilibrium characteristics
(indicated by the shape of the equilibrium curve) of the mixture will determine
the number of stages, and hence the number of trays, required for the
separation. This is illustrated clearly by applying the
McCabe-Thiele method to design a binary column. McCABE-THIELE
DESIGN METHOD The
McCabe-Thiele approach is a graphical one, and uses the VLE plot to determine
the theoretical number of stages required to effect the separation of a binary
mixture. It assumes constant molar overflow and
this implies that:
molal heats of vaporisation of the components are roughly the same
heat effects (heats of solution, heat losses to and from column, etc.) are
negligible
for every mole of vapour condensed, 1 mole of liquid is vaporised The design
procedure is simple. Given the VLE diagram of the binary mixture, operating
lines are drawn first.
Operating lines define the mass balance relationships between the liquid and
vapour phases in the column.
There is one operating line for the bottom (stripping) section of the column,
and on for the top (rectification or enriching) section of the column.
Use of the constant molar overflow assumption also ensures the the operating
lines are straight lines. Operating Line for the Rectification Section
The
operating line for the rectification section is constructed as follows. First
the desired top product composition is located on the VLE diagram, and a
vertical line produced until it intersects the diagonal line that splits the VLE
plot in half. A line with slope R/(R+1) is then
drawn from this instersection point as shown in the diagram below.
R is the ratio of reflux flow (L)
to distillate flow (D) and is called the
reflux ratio and is a measure of how much of the
material going up the top of the column is returned back to the column as
reflux.
Operating Line for the Stripping Section
The operating line
for the stripping section is constructed in a similar manner. However, the
starting point is the desired bottom product composition. A vertical line is
drawn from this point to the diagonal line, and a line of slope
Ls/Vs is drawn as illustrated
in the diagram below.
Ls
is the liquid rate down the stripping section of the column, while
Vs
is the vapour rate up the stripping section of the column. Thus the slope of the
operating line for the stripping section is a ratio between the liquid and
vapour flows in that part of the column.
Equilibrium and Operating Lines
The McCabe-Thiele
method assumes that the liquid on a tray and the vapour above it are in
equilibrium. How this is related to the VLE plot and the operating lines is
depicted graphically in the diagram on the right.
A magnified
section of the operating line for the stripping section is shown in relation to
the corresponding n'th stage in the column. L's are the liquid flows while V's
are the vapour flows. x and y denote liquid and vapour compositions and the
subscripts denote the origin of the flows or compositions. That is 'n-1'
will mean from the stage below stage 'n' while 'n+1' will mean
from the stage above stage 'n'. The liquid in stage 'n' and the vapour above
it are in equilibrium, therefore, xn and yn lie on the
equilibrium line. Since the vapour is carried to the tray above without changing
composition, this is depicted as a horizontal line on the VLE plot. Its
intersection with the operating line will give the composition of the liquid on
tray 'n+1' as the operating line defines the material balance on the trays. The
composition of the vapour above the 'n+1' tray is obtained from the intersection
of the vertical line from this point to the equilibrium line.
Number of Stages and Trays
Doing the graphical
construction repeatedly will give rise to a number of 'corner' sections, and
each section will be equivalent to a stage of the distillation. This is the
basis of sizing distillation columns using the McCabe-Thiele graphical design
methodology as shown in the following example.
Given
the operating lines for both stripping and rectification sections, the graphical
construction described above was applied. This particular example shows that 7
theoretical stages are required to achieve the desired separation.
The
required number of trays (as opposed to stages) is one less than the number of
stages since the graphical construction includes the contribution of the
reboiler in carrying out the separation.
The actual number
of trays required is given by the formula:
-
(number of theoretical trays)/(tray efficiency)
Typical values
for tray efficiency ranges from 0.5 to 0.7 and depends on a number of factors,
such as the type of
trays being used, and internal liquid and vapour flow conditions. Sometimes,
additional trays are added (up to 10%) to accomodate the possibility that the
column may be under-designed.
The Feed Line (q-line)
The diagram above
also shows that the binary feed should be introduced at the 4'th stage. However,
if the feed composition is such that it does not coincide with the intersection
of the operating lines, this means that the feed is not a saturated liquid. The
condition of the feed can be deduced by the slope of the
feed line or q-line. The q-line is that
drawn between the intersection of the operating lines, and where the feed
composition lies on the diagonal line.
Depending on the state of the feed, the feed lines will have different slopes.
For example,
- q = 0
(saturated vapour)
- q = 1
(saturated liquid)
- 0 < q < 1
(mix of liquid and vapour)
- q > 1
(subcooled liquid)
- q < 0
(superheated vapour)
The q-lines for
the various feed conditions are shown in the diagram on the left.
Using Operating
Lines and the Feed Line in McCabe-Thiele Design
If we have
information about the condition of the feed mixture, then we can construct the
q-line and use it in the McCabe-Thiele design. However, excluding the
equilibrium line, only two other pairs of lines can be used in the McCabe-Thiele
procedure. These are:
-
feed-line and rectification section operating line
-
feed-line and stripping section operating line
-
stripping and rectification operating lines
This is because
these pairs of lines determine the third.
OVERALL COLUMN DESIGN
Determining the
number of stages required for the desired degree of separation and the location
of the feed tray is merely the first steps in producing an overall distillation
column design. Other things that need to be considered are tray spacings; column
diameter; internal configurations; heating and cooling duties. All of these can
lead to conflicting design parameters. Thus, distillation column design is often
an iterative procedure. If the conflicts are not resolved at the design stage,
then the column will not perform well in practice. The next set of notes will
discuss the factors that can affect distillation column performance.
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